This paper studies the effects of monetary policy, in the sense of fully anticipated inflation, on capital formation. The relation between money and capital is a classic issue, going back to Tobin (1965), Sidrauski (1967a,1967b), Stockman (1981), Cooley and Hansen (1989,1991), Gomme (1993), Ireland (1994) and many others. All of these papers adopt reduced$form approaches: they either put money in the utility function or impose cash$in$advance con$ straints, in an attempt to capture implicitly the role of money in the exchange process, but in other respects use frictionless models. An alternative literature on money, going back to Kiy$ otaki and Wright (1989,1993), Aiyagari and Wallace (1991), Shi (1995), Trejos and Wright (1995), Kocherlakota (1998), Wallace (2001) and others, is more explicit about the frictions that make money essential, and in doing so has introduced some new elements into monetary economics, including detailed descriptions of specialization, information, matching, pricing, etc. Our goal is to see how these elements matter for the impact of inflation on investment, and other variables, including welfare. It turns out that modeling microfoundations in more detail does indeed make a difference for the quantitative results.
We build on the two$sector model in Lagos and Wright (2005), where some economic activity takes place in centralized markets and some in decentralized markets. This is useful because, in addition to providing microfoundations for the role of a medium of exchange, decentralized markets allow us to introduce ingredients like stochastic trading opportunities and bargaining, while centralized markets allow us to incorporate capital as in standard growth theory. This contrasts sharply with other attempts to study money and capital in models with frictions, including Shi (1999), Shi and Wang (2006), and Menner (2006), who build on Shi (1997), and Molico and Zhang (2005), who build on Molico (2006). Those models have only decentralized markets. It is much easier to connect with mainstream macro and to incorporate not only capital but other ingredients, like fiscal policy, in a model with some centralized trade. In particular, as a special case, in nonmonetary equilibrium, our model reduces to the textbook growth model, while those mentioned above reduce to something quite different pautarky.
Reducing the gap between models of decentralized trade and mainstream macro has been a challenge for some time. As Azariadis (1993) put it, Capturing the transactions motive for holding money balances in a compact and logically appealing manner has turned out to be an enormously complicated task. Logically coherent models such as those proposed by Diamond (1984) and Kiyotaki and Wright (1989) tend to be so removed from neoclassical growth theory as to seriously hinder the job of integrating rigorous monetary theory with the rest of macroeconomics.And as Kiyotaki and Moore (2001) put it, The matching models are without doubt ingenious and beautiful. But it is quite hard to integrate them with the rest of macroeconomic theory not least because they jettison the basic tool of our trade, competitive markets.We think the framework presented here constitutes a big step towards monetary economics with microfoundations and mainstream macroeconomics, both in terms of theory and especially in terms studying quantitative issues.
Several ingredients turn out to matter for the results. First, stochastic trading opportu$ nities are important for matching the model to the facts.2 Second, the two$sector structure is critical: in our baseline model, capital produced in the centralized market is used in the decentralized market, where money is essential, which generates interesting feedback from decentralized to centralized markets and in particular from inflation to investment. Third, perhaps surprisingly, the quantitative results depend a lot on what one assumes about price formation in the decentralized market. If we consider bargaining between buyers and sell$ ers, inflation has little impact on investment, although it has a sizable impact on welfare: going from 10% inflation to the Friedman rule barely changes the capital stock, but is worth around 3% of total consumption. Alternatively, if we consider Walrasian price taking, the same experiment increases the long$run capital stock between 3% and 5%, and has a welfare effect of 1.5% across steady states, or 1% when we take into account transitions.
It is worth emphasizing that these numbers are quite different from previous findings using reduced$form models, implying that the impact of including elements from modern monetary theory can be significant.3 We also find sizable effects from fiscal policy, although not so different from the previous literature. On balance, however, we find that if we have to make up the lost revenue with distortionary instead of lump sum taxes, reducing inflation is still a good idea, and the Friedman rule is still the best policy (contrary to some earlier reports e.g. Cooley and Hansen 1991). We also demonstrate something very new: in the bargaining version of the model, holdup problems in the demands for money and capital can be quantitatively important. This is true even if we have bargaining only in the decentralized market and this accounts less than 8% of aggregate output. Again, our conclusion is that taking into account details of the microfoundations can make a big difference for policy$ relevant quantitative issues.
The rest of the paper is organized as follows. In Section 2 we describe the model. In Section 3 we discuss calibration. In Section 4 we present quantitative results. In Section 5 we conclude. The Appendix contains details of the analysis and alternative specifications.
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